Q. J. R. Meteorol. Soc. (2002), 128, pp. 337–360 Lagrangian description of airows using Eulerian passive tracers By FRANC ¸ OIS GHEUSI and JO ¨ EL STEIN ¤ M´ et´ eo-France, France (Received 2 October 2000; revised 17 July 2001) SUMMARY A method of tracking coherent Lagrangian airmasses is presented. It is not based on the computation of individual trajectories, but rather on three Eulerian passive tracers initialized with the coordinates of each grid cell. This ‘initial coordinates’ method allows the later unambiguous identication of each Lagrangian air parcel by referring to its initial position. Further, the physical history of each parcel can be retrieved. The advantages of this method in the framework of mesoscale numerical modelling are discussed with respect to trajectory-based methods. Preliminary examples are given by studying idealized airows: (i) a two-dimensional stratied ow past an isolated obstacle generating gravity-wave breaking; (ii) a deep convective squall line. Then the method is applied to a heavy-rain situation over the Alps during the Mesoscale Alpine Programme (MAP) eld phase. A coherent mesoscale pool of dry air is identied over the Mediterranean and tracked with the aid of the initial- coordinates method. Its inuence on the rain distribution over the Ligurian Alps and Apennines is demonstrated. KEYWORDS: Lagrangian tracking Mesoscale Alpine Programme Orographic precipitaion 1. I NTRODUCTION The Lagrangian perspective is widely used in the framework of the atmospheric sciences. The tracking of air parcels enables the identication of ‘coherent ensembles of trajectories’ (Wernli and Davies 1997), dened as ensembles of air parcels which experience a common physical history and may have a signicant inuence on the circulation. The most common technique for the Lagrangian description of an airow is the calculation of trajectories, using wind elds extracted from either analysis systems, global circulation models or limited-area models. For instance, trajectories calculated from analyses have proved to usefully complement Eulerian diagnostic techniques for the study of ow structure in the troposphere and stratosphere, when long-range transport over several days is considered (e.g. Wernli and Davies 1997). High-resolution numerical modelling over shorter time ranges has appeared to be an efcient tool for capturing some features of the dynamics of airows at the mesoscale. When the question of Lagrangian tracking is considered in this framework, some drawbacks of the trajectory technique can be listed in terms of implementation, treatment and accuracy. Most atmospheric models are based on the equations of uid mechanics in their Eulerian form. A specic numerical model of trajectories is then needed in addition to the Eulerian model. The wind elds generated by the Eulerian model are required at every time step of the trajectory model. Thus, as explained by R¨ ossler et al. (1992), trajectories can either be computed in parallel with the Eulerian model run (run-time method, hereafter ‘RT method’), or post-processed from the model outputs (post- mortem method, hereafter ‘PM method’). Compared with the RT method, the PM method has the advantage of allowing calculations of forward as well as backward trajectories. The number of calculated trajectories rarely exceeds a few hundred, well below the number of model grid cells. The trajectories hence provide a small part of the available Lagrangian information. Moreover, if parcels are arbitrarily chosen, only a few ¤ Corresponding author: M´ et´ eo-France CNRM/GMME/Relief, 42 Av. Coriolis, 31057 Toulouse Cedex, France. e-mail: Joel.Stein@meteo.fr c ° Royal Meteorological Society, 2002. 337